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Prove that the determinent |{:(x,sinthet...

Prove that the determinent `|{:(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x):}|` is independent from value of `theta`

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The correct Answer is:
`-x^3`
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KUMAR PRAKASHAN-DETERMINANTS -MISCELLANEOUS EXERCISE - 4
  1. Prove that the determinent |{:(x,sintheta,costheta),(-sintheta,-x,1),(...

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  2. Without expanding the determinant prove that |{:(a,a^2,bc),(b,b^2,ca),...

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  3. Evaluate |{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosb...

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  4. If a, b and c are real numbers , and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b...

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  5. Solve the equation |{:(x+a,x,x),(x,x+a,x),(x,x,x+a):}|=0. (ane0)

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  6. Prove that |{:(a^2,bc,ac+c^2),(a^2+ab,b^2,ac),(ab,b^2+bc,c^2):}|=4a^2b...

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  7. If A^(-1)=[{:(3,-1,1),(-15,6,-5),(5,-2,2):}] and B=[{:(1,2,-2),(-1,3,0...

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  8. Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}] Verify that [adjA]^(-1)=adj(A^...

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  9. Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}] Verify that (A^(-1))^-1=A

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  10. Evaluate |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|

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  11. Evaluate |{:(1,x,y),(1,x+y,y),(1,x,x+y):}|

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  12. Using properties of determinants in Exercise 11 to 15 prove that |{:...

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  13. Using properties of determinants in Exercise 11 to 15 prove that |{:...

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  14. Using properties of determinants in Exercise 11 to 15 prove that |{:...

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  15. Using properties of determinants in Exercise 11 to 15 prove that |{:...

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  16. Using properties of determinants in Exercise 11 to 15 prove that |{:...

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  17. Solve the following system of linear equations 2/x+3/y+(10)/z=4 4/...

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  18. If a,b,c are in A.P then the determinant |{:(x+2,x+3,x+2a),(x+3,x+4,...

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  19. If x,y,z are nonzero real numbers, then the inverse of matrix A=[{:(x,...

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  20. Let A=[{:(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1):}] w...

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